|
Titel |
Scale-invariant Horizontal Diffusion in a Global Circulation Model |
VerfasserIn |
Urs Schaefer-Rolffs, Erich Becker |
Konferenz |
EGU General Assembly 2011
|
Medientyp |
Artikel
|
Sprache |
Englisch
|
Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 13 (2011) |
Datensatznummer |
250048391
|
|
|
|
Zusammenfassung |
General Circulation Models (GCMs) are powerful tools to understand the dynamics of the
general circulation of the atmosphere. A large amount of the kinetic energy (KE)
produced by baroclinic waves is dissipated in the boundary layer. However, about
one quarter of the KE is dissipated in the free atmosphere mainly by horizontal
momentum diffusion. In GCMs this diffusion is often represented by an empirical
hyper-diffusion scheme or by a numerical filter. It is well known that a reasonable
simulation of the global circulation is not possible without such a scale-sensitive
damping.
In this presentation we propose an improved parametrization of the horizontal diffusion.
Until now, we have used the Smagorinsky scheme in the Kühlungborn Mechanistic general
Circulation Model (KMCM), i.e. a harmonic diffusion based on the mixing length concept.
The disadvantage of this approach is that it is not scale-invariant, neither in the synoptic nor
in the mesoscale inertial range. The reason is the assumption of a constant mixing length.
We replace this scheme by the Dynamic Smagorinsky Model (DSM), which is
usually used in boundary layer theory. To the best of our knowledge, the DSM
approach has never been used in a GCM as a parametrization of horizontal momentum
diffusion.
The DSM provides a calculation of the local mixing length in dependence on the resolved
flow. The method is based on evaluating the difference of the turbulent stress from two
different resolutions by means of a test filter. This difference yields the turbulent stress due to
the smallest resolved scales of the flow and should also be parameterized with the
Smagorinsky approach. This constraint yields a local mixing length for the unresolved scales
that ensures scale invariance. To ensure a positive dissipation rate, we use, unlike most other
simulations, a tensor norm approximation to solve the basic tensor equation of the
DSM.
Strong motivation for the use of the DSM is given by the fact that, in contrast to the often
used hyper-diffusion schemes, it is like the classical Smagorinsky approach fully
compatible with the hydrodynamic conservation laws. Surprisingly, the DSM has the
counter-intuitive effect that the mixing length scales with the inverse wave number of
the currently largest spectral component of the velocity field. Some preliminary
results from a mechanistic climate simulation with the KMCM will be presented. |
|
|
|
|
|